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Mathematics

Grade9

Easy

Question

In an isosceles triangle ABC with AB = AC, if BD and CE are the altitudes, then BD and CE are______.

Perpendicular to each other
Not equal to each other
Equal to each other
Parallel to each other

hint Hint:

In this question we have to determine the relation between BD and CE. For this we can look the triangles where BD and CE belongs, that is $increment A B D space a n d space increment A C E$ and prove them congruent. After which we can determine their relation.

The correct answer is: Equal to each other

In an isosceles triangle ABC with AB = AC, if BD and CE are the altitudes, then BD and CE are equal to each other __.

$I n space increment A B D space a n d space increment A C E comma angle A D B equals angle A E C left parenthesis B D space a n d space C E space a r e space a l t i t u d e s space t o space A C space a n d space A B space r e s p. space right parenthesis angle A equals angle A left parenthesis c o m m o n right parenthesis A B equals A C left parenthesis g i v e n right parenthesis S o comma space increment A B D space approximately equal to space increment A C E left parenthesis b y space A A S right parenthesis S o comma space B D space equals C E space left parenthesis b y space c p c t right parenthesis$

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